A pressure fluid pumping device is already known (German Patent Application P 39 07 927.4) in which at least two diametrically opposed outlet bores of an outlet conduit for pressure fluid lead from the relatively small-volume hollow space of the housing of an outlet valve having a ball as its valve closing body, into a chamber of a pump housing. This chamber has a relatively large volume and communicates downstream, through a throttle bore, with a pressure fluid line. With its embodiment, because of the compressibility of the pressure fluid in the chamber and the elasticity of the pump housing wall defining the chamber, damping of the pulsations in the flow of pressure fluid unevenly expelled from the reciprocating piston pump is attained. Nevertheless, the known pressure fluid pumping device is not entirely satisfactory in terms of noise because the outlet valve opens abruptly in the pumping stroke of the reciprocating piston pump until the valve opening cross section is completely opened. As a result, not only are there compression impacts but also abrupt variations in force in the drive train of the reciprocating piston pump, this generating noise that is transmitted as structureborne sound to the structural parts, for instance of a motor vehicle, that carry the pressure fluid pumping device and is difficult to damp.